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A theory of thin films of martensitic materials with applications to microactuators. (English) Zbl 0960.74046
From the summary: We give a direct derivation of a theory for single crystal thin films, starting from three-dimensional nonlinear elasticity augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwinned austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations – “tents” and “tunnels” – that could possibly be the basis of simple large-deformation microactuators.

MSC:
74K35Thin films (solid mechanics)
74G65Energy minimization (equilibrium problems in solid mechanics)
74A35Polar materials
74N05Crystals (solid mechanics)